Valuation Uncertainty and Disagreement in OTC Derivatives Markets: Evidence from Markit’s Totem Service Jon Danielsson, Lerby Ergun, Andreas Uthemann, and Jean-Pierre Zigrand Systemic Risk Centre, LSE
November 19, 2015
Models and Valuation Uncertainty in OTC Derivatives Markets I
In OTC derivatives markets, market participants’ beliefs about asset valuations are typically encoded explicitly in “pricing models”
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“pricing model” ≈ parameterised price processes for assets underlying the derivative together with “no arbitrage” conditions
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Model parameters are calibrated to market prices available from liquid instruments
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Asset valuations for instruments where market data is sparse often obtained from calibrated models (“mark-to-model” rather than “mark-to-market”)
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Disagreement on asset values across market participants most likely observed in regions where market data is sparse/absent (e.g. option contracts on extreme events)
Why Worry about Model Disagreement?
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Understanding of “model risk” for certain products essential for appropriate risk management (e.g. margin requirements for CCPs): How dependent are risk measures on the specification of asset price processes?
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Disagreement between market participants as an indicator for fundamental (Knightian) uncertainty about an asset’s payoff distribution.
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In OTC derivatives markets, participants “communicate” through models (e.g. IVs from Black-Scholes model in the options market (MacKenzie, 2008)). A degree of common understanding might be essential for price formation process.
Objectives of Research
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Provide empirical evidence on the extent of disagreement on asset valuations in OTC derivatives market.
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Empirical analysis will focus on option contracts for major equity indices
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Examine valuation disagreement on option prices in the time-to-maturity / moneyness space.
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We document increase in disagreement on option valuations when we move “out-of-the-money” and into longer terms.
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Disagreement between market participants is also more persistent in these regions.
Challenges for Empirical Work: Data Availability
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Publicly available data on prices & quantities sparse for most OTC markets. Most transaction data is proprietary.
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Some recent initiatives to improve transparency through mandatory trade reporting (e.g. TRACE for US bond market; EMIR, Dodd-Frank for OTC derivatives market).
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Fundamental challenge for empirical work remains: illiquid markets tend to have few transactions.
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The most critical market episodes might be the ones without transactions: market freezes, liquidity dry-ups...
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Ideally we would want to know market participants’ beliefs about asset values irrespective of frequency of trading.
Consensus Data: Markit Totem Service
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Markit Totem is a data service providing consensus prices to major OTC derivatives market-makers
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Consensus prices are neither transaction prices, nor firm quotes. They are price estimates for specific assets coming from market participants (see next slide).
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The Totem service covers a broad range of asset classes and enables market-makers to check their book valuations in the absence of liquid market prices.
Totem Data Data Proccess
Markit
Client Valuation +
Spread Sheet
Parameters
SRC @ Markit
Individual
Resubmission
Submissions Markit Cleaning Create
Client
Consensus
Consensus SRC
Data: Consensus Prices for Index Options
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We concentrate on plain-vanilla European put and call options on major equity indices: S&P 500, FTSE 100, Nikkei 225, and Euro Stoxx 50.
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Totem provides consensus data for times to maturity of up to 25 years, and moneyness (strike/spot price) ranging from 20 to 300. Why look at index options?
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I
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volatility surface central to calibrating price processes used for pricing variety of exotic derivatives options vary in liquidity in the moneyness/maturity space, but homogenous underlying model structure
Consensus Pricing
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p TOTEM submitters submit monthly price quotes yi,t for a range of derivatives contracts C
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c designates the TOTEM quote for submitter i at time t for yi,t contract c ∈ C .
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The TOTEM consensus price for c at t with Ntc submitters is (ignoring data cleaning) c
y¯tc
Nt 1 X c yi,t = c Nt i=1
A First Look at the Data
Figure : Consensus IVs, Put Option (moneyness 80) on FTSE 100
Measuring Disagreement Holding c fixed (i.e. term,moneyness, and index) we decompose c s total (quadratic) variation in all submitters yi,t Vwc =
Ti N X X
c (yi,t − y¯ c )2
i=1 t=1
where y¯ c =
1 N
i
y¯ic and y¯ic =
1 Ti
c t yi,t . PN PTi c = c I into Within Variation: Vw ¯ic )2 t=1 (yi,t − y i=1 PN I and Between Variation: V c = yic − y¯ c )2 i=1 Ti (¯ b I Use V c /V c as a measure of disagreement for contract b
P
P
c: How important are valuation disagreements between submitters compared to time-series variation in individual submissions?
Volatility Surface Decomposed: Between-to-Total Variation
Figure : Vbc /V c for S&P 500 index options (Jan 2010 - Dec 2014)
(a) S&P 500
(b) FTSE 100
(c) Nikkei 225
(d) Euro Stoxx 50
Figure : contour plots for major equity indices (2010-2014)
What is Nature of Disagreement
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p We now consider deviations from consensus price yi,t − y¯tp
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Suppose submitters every month start from common prior, and each receives (short-lived) private information:
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Submitter i receives private signal Si,t = Yt + ηi,t with ηi,t ∼ N(0, 1/ρi,t ).
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Submitter i’s information set in t: Ii,t = {Si,t , It−1 }
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N consensus price submitters, each submitting yi,t in t with yi,t = E(Yt |Ii,t ). yi,t = (1 − λi,t )ˆ yt + λi,t Si,t = yˆt + λi,t ui,t where λi,t = ρi,t /(ρi,t + ρt ) and ui,t = Si,t − E(Yt |It−1 ).
Empirical Implications I
The consensus price in period t is y¯t =
N 1 X yj,t N j=1
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Individual deviations from consensus are then N − 1 1 X ¯ t )vt + yi,t − y¯t = (λi,t − λ λi,t εi,t + λj,t εj,t N N j6=i
where ui,t = vt + εi,t . I
Moment condition: E [(yi,t − y¯t )zt−1 ] = 0 for all zt−1 ∈ It−1
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Moment condition suggests the following setup: yi,t − y¯t = α + β T zt−1 + i,t H0 : α = 0 and β = 0 for all zt−1 ∈ It−1 .
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Reject H0 for all contracts c in moneyness/term space.
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Particularly, lagged deviation yi,t−1 − y¯t−1 always significantly different from 0.
How persistent are disagreements? I
Estimate AR(1) model to examine persistence of individual deviations from consensus
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For each contract c in the term/moneyness space we estimate c c c yi,t − y¯tc = β c yi,t−1 − y¯t−1 + εci,t pooled across submitters.
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Calculate half-life from coefficients β c −
log 2 log β c
How many month does it take to close 1/2 of an initial gap between individual submission an consensus?
How persistent are deviations from consensus?
Figure : Half-lifes (in months), S&P 500 (2010-2014)
(a) S&P 500
(b) FTSE 100
(c) Nikkei 225
(d) Euro Stoxx 50
Figure : Half-lifes of deviations from consensus (2010-2014)
Summary of Results I
We provide (preliminary) evidence on the extent of disagreement on valuations in the market for index options
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Using TOTEM consensus price data we show that disagreement increases the further we move “out-of-the-money” or in “time-to-maturity” ≈ “illiquid” part of the market
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Persistence of disagreement also increases in this direction
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Given the nature of pricing in the options market, we interpret disagreement as differences in pricing models used by market participants
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Agreement is observed in areas where model can be calibrated to market data, disagreement where no reliable data exists
Number of TOTEM Submitters (2010-2014)
(a) S&P 500
(b) FTSE 100
(c) Nikkei 225
(d) Euro Stoxx 50
